Robotics Research Technical Report: Mountain Climbing, Ladder Moving, and the Ring-Width of a Polygon (Classic Reprint) - Tapa blanda

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Excerpt from Robotics Research Technical Report: Mountain Climbing, Ladder Moving, and the Ring-Width of a Polygon

Proof: Replace 1' by a tubular neighborhood I' of sufficiently small radius 6. Then, starting at A, run along the boundary of f Eventually we must either return to A or arrive at C, since the total number of arcs is finite and we cannot repeat a previous position. In the first case the path itself (together with part of the boundary of S) constitutes a path from B to D which avoids P, and in the second case the corresponding arcs of I'

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